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Computing the nearest reversible Markov chain
"... Computing the nearest reversible Markov chain ..."
On nonreversible Markov chains
 Institute Communications, Volume 26: Monte Carlo Methods
, 2000
"... . Reversibility is a sufficient but not necessary condition for Markov chains for use in Markov chain Monte Carlo simulation. It is necessary to select a Markov chain that has a prespecified distribution as its unique stationary distribution. There are many Markov chains that have such property. We ..."
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Cited by 7 (1 self)
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. Reversibility is a sufficient but not necessary condition for Markov chains for use in Markov chain Monte Carlo simulation. It is necessary to select a Markov chain that has a prespecified distribution as its unique stationary distribution. There are many Markov chains that have such property
Symmetry analysis of reversible markov chains
 INTERNET MATHEMATICS
, 2005
"... We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools involving a group commuting with a selfadjoint operator with criteria for an eigenvector to descend to ..."
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Cited by 55 (15 self)
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We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools involving a group commuting with a selfadjoint operator with criteria for an eigenvector to descend
Reversible Markov Chains
, 1994
"... ly, call f : [0; 1) ! [0; 1) completely monotone (CM) if there is a nonnegative measure on [0; 1) such that f(t) = Z 1 0 e \Gamma`t (d`); 0 t ! 1: (41) Our applications will use only the special case of a finite sum f(t) = X m am e \Gamma` m t ; for some am ; ` m 0: (42) but finiten ..."
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Cited by 12 (0 self)
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ly, call f : [0; 1) ! [0; 1) completely monotone (CM) if there is a nonnegative measure on [0; 1) such that f(t) = Z 1 0 e \Gamma`t (d`); 0 t ! 1: (41) Our applications will use only the special case of a finite sum f(t) = X m am e \Gamma` m t ; for some am ; ` m 0: (42) but finiteness plays no essential role. If f is CM then (provided they exist) so are \Gammaf 0 (t) F (t) j Z 1 t f(s)ds (43) A probability distribution on [0; 1) is called CM if its tail distribution function F (t) = (t; 1) is CM; equivalently, if its density function f is CM (except here we must in the general case allow the possibility f(0) = 1). In more probabilistic language, is CM iff it can be expressed as the distribution of =, where and are independent random variables such that has exponential(1) distribution; ? 0: (44) 19 Given a CM function or distribution, the spectral gap 0 can be defined consistently by = infft ? 0 : [0; t] ? 0g in setting (41) = minf`m g in setting...
Some inequalities for reversible Markov chains
 J. London Math. Soc
, 1982
"... One of the most important results about finite ergodic Markov chains is the convergence of transition probabilities to the stationary distribution. The object of this paper is to investigate relations between the time taken to approach stationarity and certain properties of mean hitting times. Our m ..."
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Cited by 69 (7 self)
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One of the most important results about finite ergodic Markov chains is the convergence of transition probabilities to the stationary distribution. The object of this paper is to investigate relations between the time taken to approach stationarity and certain properties of mean hitting times. Our
Analysis of a NonReversible Markov Chain Sampler
, 1997
"... We analyse the convergence to stationarity of a simple nonreversible Markov chain that serves as a model for several nonreversible Markov chain sampling methods that are used in practice. Our theoretical and numerical results show that nonreversibility can indeed lead to improvements over the dif ..."
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Cited by 54 (7 self)
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We analyse the convergence to stationarity of a simple nonreversible Markov chain that serves as a model for several nonreversible Markov chain sampling methods that are used in practice. Our theoretical and numerical results show that nonreversibility can indeed lead to improvements over
Metastability and low lying spectra in reversible Markov chains
 Comm. Math. Phys
"... Abstract: We study a large class of reversible Markov chains with discrete state space and transition matrix PN. We define the notion of a set of metastable points as a subset of the state space ΓN such that (i) this set is reached from any point x ∈ ΓN without return to x with probability at least ..."
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Cited by 55 (14 self)
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Abstract: We study a large class of reversible Markov chains with discrete state space and transition matrix PN. We define the notion of a set of metastable points as a subset of the state space ΓN such that (i) this set is reached from any point x ∈ ΓN without return to x with probability at least
Results 1  10
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633,849